document.write( "Question 1134204: solve for x. 6^(3x-4) 2^(2x+3)=648(48)^x \n" ); document.write( "
Algebra.Com's Answer #751536 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"6%5E%283x-4%29%2A2%5E%282x%2B3%29=648%2848%29%5Ex\"\r\n" );
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document.write( "Take logs of both sides  (can take natural logs instead if preferred)\r\n" );
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document.write( "\"log%28%286%5E%283x-4%29%2A2%5E%282x%2B3%29%29%29=log%28%28648%2848%29%5Ex%29%29\"\r\n" );
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document.write( "Use the product-to-sum log fact on both sides:\r\n" );
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document.write( "Use the exponent-to-multiplier log fact on both sides:\r\n" );
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document.write( "Let's break three of those logs down to the side:\r\n" );
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document.write( "     1.  \r\n" );
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document.write( "     2. \r\n" );
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document.write( "     3.  \r\n" );
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document.write( "Those are all in terms of log(2) and Log(3). \r\n" );
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document.write( "To keep from getting bogged down with too many complicated symbols,\r\n" );
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document.write( "let A = log(2) and let B = log(3), then\r\n" );
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document.write( "     1.  \"log%28%286%5E%22%22%29%29=log%28%282%5E%22%22%29%29%2Blog%28%283%5E%22%22%29%29=A%2BB\"\r\n" );
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document.write( "     2. \r\n" );
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document.write( "     3. \"log%28%2848%5E%22%22%29%29=4%2Alog%28%282%5E%22%22%29%29%2Blog%28%283%5E%22%22%29%29=4A%2BB\" \r\n" );
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document.write( "Now go back to the equation:\r\n" );
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document.write( "and substitute the expressions in A and B for the logs:\r\n" );
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document.write( "\"%283x-4%29%28A%2BB%29%2B%282x%2B3%29%28A%29=%283A%2B4B%29%2Bx%2A%284A%2BB%29\"\r\n" );
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document.write( "Multiply out:\r\n" );
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document.write( "\"%283Ax%2B3Bx-4A-4B%29%2B%282Ax%2B3A%29=3A%2B4B%2B4Ax%2BBx\"\r\n" );
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document.write( "\"3Ax%2B3Bx-4A-4B%2B2Ax%2B3A=3A%2B4B%2B4Ax%2BBx\"\r\n" );
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document.write( "Combine like terms on the left:\r\n" );
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document.write( "\"5Ax%2B3Bx-A-4B=3A%2B4B%2B4Ax%2BBx\"\r\n" );
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document.write( "Get all the terms in x on the left and all the others on the right:\r\n" );
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document.write( "\"5Ax%2B3Bx-4Ax-Bx=A%2B4B%2B3A%2B4B\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"Ax%2B2Bx=4A%2B8B\"\r\n" );
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document.write( "Factor out x on the left side and 4 out of the right side:\r\n" );
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document.write( "\"x%28A%2B2B%29=4%28A%2B2B%29\"\r\n" );
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document.write( "Divide both sides by (A+2B)\r\n" );
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document.write( "\"x=4\"\r\n" );
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document.write( "Edwin
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